Astro Maven Blog
Blog of Rick Boozer, astrophysicist
On Twitter: rboozer
Also on Facebook and LinkedIn

Translate

Friday, December 12, 2014

Photometry with AIP4WIN: a TutorialPart 4 - Image Calibration

By R.D. Boozer

The following three images depict actual
final master frames produced when AIP4WIN processed the supplied raw FITS
files.

Figure 14: The final master bias frame.

Figure 15: The final scaling master dark
frame

Figure 16: Final master flat-field frame
with the V filter.

The master bias and scaling master dark
frames shown in Figures 14 and 15 do not really
reveal any important information to a human viewing them.They don’t need to.They exist solely for the software to
optimize the image by eliminating electronically generated artefacts that are
beyond a human being’s control.

However,
the master flat-field frame is a different story since it may sometimes reveal
problems that are the result of human negligence.In the illustration depicting the master
flat-field frame, I have labelled a number of common mostly minor issues that
seldom cause serious problems, since the purpose of the master flat-field frame
is to counter those effects.Nevertheless, sometimes imperfections happen due to simple carelessness
and may be so severe that flat-fielding will have difficulty fully correcting
them.Such is probably the case with the
small solid grey oval labelled “?” that appears near the bottom of the frame
whose darker color indicates that pixels within it got a much lower photon hit
rate than they should have.As shall be
mentioned later, in regard to an unrelated issue wherein I suspected a bug in
AIP4WIN, I sent copies of my master bias, master dark, and master flat-field
frames to Richard Berry in his role as lead user supporter of AIP4WIN.In a side comment, Mr. Berry brought notice
to the oval saying, “… [it] looks suspiciously like someone sneezed on the
optical window of the CCD camera.”Though the flat-field frame may correct for most of the inaccuracy
caused by such carelessness, it by no means does a perfect job.

The
reader may have noticed another tab in the series in the Calibration
Setup Tool that is labelled Defect.This is used to repair cosmetic problems on
images that are not used for scientific purposes.Applying this function to images used for
astrometry or photometry will compromise the integrity of the image data.
(Berry and Burnell 204)

All V filter images were shot with an
integration time of 20 seconds.The
created master bias frame, scaling master dark frame and V filter master
flat-field frame were used to calibrate every V filter stellar image via the Auto-calibrate
option under the Calibrate menu.An uncalibrated V filter image that has just been loaded is displayed in
Figure 17 with calibration imminent.

Figure 17: A raw image is about to be
calibrated.

As soon as the Auto-calibrate option
is clicked, all of the master calibration files are applied to the raw stellar
image.That is, the master bias frame is
subtracted from it, the scaling master dark frame is scaled to match the
image’s exposure time and then subtracted, and the image’s pixels have the
previously described flat-field scaling algorithm applied to them using the
master flat-field frame.An image that
has been fully calibrated in such a manner is shown in Figure 18.

Figure 18: A fully calibrated image.

The
letter ‘V’ in the middle of the filename shown in the title bar above the image
designates that it is a V filter image.Of course for I filter and R filter images, there will be either an ‘I’
or ‘R’ in that position.The rightmost
two digits indicate where in the chronological sequence that an image fits;
i.e., image 03 above will be followed by image 04, etc. I added “CF” to the
filename to indicate that it had been calibrated with bias and dark frames and
with flat-fielding applied.I was
initially disturbed when I saw that the calibrated image came up on the screen
with a low contrast or “washed out” appearance and I suspected either a bug in
AIP4WIN or that I prepared one or more of the master frames incorrectly.It was at this point when I sent copies of
his master frames and an image calibrated with them to Richard Berry, co-author
of and lead user supporter for AIP4WIN.Berry offered assurance that I had produced a good calibrated image and
went on to remark in the same email, “Always think QUANTITATIVELY with
astronomical images -- never trust the appearance on the screen.”Though I found Berry’s comments somewhat
reassuring, I felt the need to empirically prove that the calibrated image was
significantly better than the original.After some consideration, I came up with the idea of seeing if there was
a significant improvement in signal-to-noise ratio going from the raw image to
the calibrated one.

Figure 19: Getting the SNR of a star in the
raw image.

As shown in Figure 19, the Single
Star Photometry function was used on a raw image.It was invoked under the Measure
menu by clicking the Photometry option and then choosing the Single
Star suboption.The last action
caused the depicted dialog box to appear.After a star is clicked in the image, a number of data are given under
the Details tab, one of which is the signal-to-noise ratio of the
selected star that is indicated to be around 65.Next an identical series of actions were
repeated for the calibrated image using the same star.

Figure 20: Getting the SNR of the same star
in the calibrated image.

The SNR of the same star in the calibrated
image is about 152.Approximately 2.4
times greater than in the raw image!It
appears that calibration was indeed a success.

Two V filter images were immediately rejected
without even checking them I was told beforehand that Gliese 876 was saturated
in those images: X2253V2470028.fits, and X2253V2470048.fits.It should also be mentioned that all other
images exposed with all filters were examined to see whether or not they
contained a saturated star image.The
procedure that I followed for determining this condition will now be outlined.

Figure 21: Checking for saturation of
Gliese 876.

First, the image to be checked was loaded and
the Single Star Photometry function was invoked as described
earlier; however, the Result tab was used this time.The brightest star in the image (that was
always Gliese 876) was clicked.In the
case of all other V images, I found that the peak pixel value for that star was
significantly less than the saturation value of 65535.As an educated guess, I would say that since
the flat frame cannot do a perfect correction for pixel variation, any image
should be rejected if the peak of the target star is higher than the upper
50,000s.In Figure 21,
one can see that the star’s peak pixel value is 41973.9 and so the image is a
good candidate for photometry.

In the V filter images, the target star,
Gliese 876, is the most prominent star.In a few of the images, either only one star other than the target star
is visible or some others were fairly faint.In all of the rest of the images four other stars are prominently
visible.Figure 22
depicts one of the worst images where there is only one star other than Gliese
876 that is plainly visible and that is the star to the far right.

Figure 22: One of several V images that
show only one other star than Gliese 876.

Why are there some images where only the
target star and one other star are prominent, though in the remaining images
the other stars are plainly visible?If
seeing conditions were relatively constant throughout the night, there should
be the same number of prominent stars visible in each frame, since the images
were all shot with the same integration time.

The two worst offenders are images
X2253V2470001 and X2253V2470004.To
investigate what is going on, I looked closely at these images and compared
them to images where more stars were prominent.

For example, the fact that only the brightest
stars are showing in image X2253V2470004 might lead me to suspect that a thin
cloud layer obscures the other stars.But is there a way to empirically prove that?To get the necessary evidence to check this
hypothesis, a test was done.A
comparison was made between image number X2253V2470004 (which is depicted in Figure
22 as a one of the frames showing only Gliese 876 and the comparison
star) and image X2253V2470005 (that is one of the frames showing at least five
prominent stars).

The light profile of the star to the right of
Gliese 876 in the five star image X2253V2470005 appears in Figure 23.

Figure 23: Light profile of a star from an
image showing several stars.

The above pictured dialog box was invoked by
going to the Measure menu, clicking the Star Image Tool
option, selecting the Shape tab and finally clicking the star to be
measured.This causes a plot of ADU
counts for the star at increasing pixel radii from the centre of the star.

Now compare the plot above to the plot of the
light profile of the same star in the two star image X2253V2470004 that follows
in Figure 24.

Figure 24: Light profile of C1 from an
image showing only two stars.

Notice how the light profile of the same star
obtained from the image with several stars is relatively tight and thin, whilst
the other light profile from the image with only two stars has a curve that is
thicker and more diffuse.The latter
curve is exactly the kind of curve one would expect to see if the starlight is
being diffused by a cloud!Light that
would have been thinly concentrated at each particular radius is being
scattered by cloud particles over several radii.X2253V2470001 is another image with only two
prominent stars and it too showed a “fuzzy” light profile similar to Figure
24.

The light profile of the same star in images
X2253V2470003, X2253V2470045 and X2253V2470049 also shows a lot of fuzziness,
but the curve line is not as thick in these and would indicate that the cloud
layer was thinner than it was when images X2253V2470001 and X2253V2470004 were
taken.The inescapable conclusion: a
cloud layer is the culprit for the severe magnitude discrepancies.

It is a well established precedent that
accurate differential photometry may be carried out through “haze or light
clouds” (Berry and Burnell 293)Given
that fact, was the haze or cloud level thin enough in the remaining images to
allow the possibility of valid results?The accepted practice to check for this condition is to make sure that
the target star and at least one other star has a signal-to-noise ratio of 100
or greater.(Berry and Burnell 296)This issue is very important because SNRs of
100 or higher are required to obtain accurate data on a light curve with an
amplitude around 0.1 magnitudes or below, such as extrasolar planetary
transits. (Warner 34)After performing
this check on all of the V filter images, the only images that did not meet
this qualification were X2253V2470001, X2253V2470003, X2253V2470045 and
X2253V2470049.Therefore, if these are
excluded from the set, what is left is a set of images suitable for
differential photometry for this project.However, even these images are such that the remaining 3 prominent stars
have SNRs far below 100, meaning a restriction to having only one comparison
star.

Because there were no comparison images of
parts of the sky other than the field containing the target, it is obvious that
the University of Tasmania observers intended differential photometry to be
used in their analysis. In my opinion
this was a wise decision because differential photometry has three primary
advantages: 1) accurate differential photometry may be done through thin
clouds, 2) it is simpler to implement than other methods (Warner 32) and 3)
atmospheric extinction issues affect it less than any of the other photometric
methods.In fact, as long as the target
and comparison star have similar colors, atmospheric extinction effects are
essentially totally eliminated!This
condition is true because all stars in the image are of necessity shot through
the same filter, at the same time and are close enough to each other that they
are thus subject to essentially the same airmass. (Berry and Burnell 279,
Warner 32-33)Unfortunately, it is not
always possible for the target star and comparison star to be of similar
colour, and this issue will be discussed later.

The importance of point number 3 above cannot
be over emphasized.It implies some
important principles that will be empirically obvious in the final photometric
data shown later in this tutorial.The
most basic of these principles is that the difference between the
observed magnitudes of the comparison star and target star is relatively
insensitive to atmospheric changes such as cloud variation and airmass
extinction.Since the comparison star is
considered to be of constant brightness, any variation in the difference of
the magnitudes should be coming only from the target star.However, changes in cloud cover and airmass
will cause wide variations in the observed raw magnitude of the target
star.Ergo, the difference in
magnitudes between the comparison star and the target star is a much more reliable
indicator of real changes in the magnitude of the target star than the target
star’s observed raw magnitude.

In the next instalment of this tutorial, the
method of setting up the actual differential photometry using the Magnitude
Measurement Tool will be described in detail.

No comments:

Post a Comment

I give public presentations on astronomy and space travel.

Congressional pork barrel politics are keeping NASA from doing great things in space. Find out what the culprits are doing and what can be done to fix the problem. Read The Plundering of NASA: an Exposé. Acclaimed by noted space industry professionals.